Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.y=sqrt(x - 2) - 1

The garden is made up of a rectangular patch of grass and two semi-circular vegetable patches. If the dimensions of the rectangular patch are 16 m (length) and 8 m (width) respectively, calculate: a) the perimeter of the garden.
b) the total area of the garden.

Given $f(x)=x^2$, after performing following transformations shift upwards 18 units and shift 89 units to the right, the new function g(x)=?

Starting with the function $f(x)=e^x$, create a new function by performing the following transformations.
i. First shift the graph of f (x) to the left by two units.
$f_1(x)=$?
ii. Then compress your result by a factor of $1/7$
$f_2(x)=$ ?
iii. Next, reflect it across the x-axis.
$f_3(x)=$ ?
iv. And finally shift it up by eight units to create g (x).
g (x) =?

Your friend attempted to describe the transformations applied to the graph of $y=\sin x$ to give the equation $f(x)=\frac{1}{2}\sin (-\frac{1}{3}(x+30))+1$.
They think the following transformations have been applied. Which transformations have been identified correctly, and which have not? Justify your answer.
a) f(x) has been reflected vertically.
b) f(x) has been stretched vertically by a factor of 2.
c) f(x) has been stretched horizontally by a factor of 3.
d) f(x) has a phase shift left 30 degrees.
e) f(x) has been translated up 1 unit.

Determine the transformations of the function f(x) to get the function $g(x)=1/2f(5(x-3))-12$ (The transformations happen in c, b, a, d order)

Create a new function in the form $y=a(x-h{)}^2+k$ by performing the following transformations on $f(x)=x^2$.
Give the coordinates of the vertex for the new parabola.
g(x) is f (x) shifted right 7 units, stretched by a factor of 9, and then shifted down by 3 units. g(x) = ?
Coordinates of the vertex for the new parabola are:
x=?
y=?

Sketch the graph of the function $f(x)=-2^x+1+3$ using transformations. Do not create a table of values and plot points